Calculus of Variations and Geometric Measure Theory

A. Cesaroni - M. Cirant

Brake orbits and heteroclinic connections for first order Mean Field Games

created by cesaroni on 12 Dec 2019
modified on 01 Jul 2021


Published Paper

Inserted: 12 dec 2019
Last Updated: 1 jul 2021

Journal: Trans. Amer. Math. Soc.
Volume: 374
Number: 7
Pages: 5037-5070
Year: 2021

ArXiv: 1912.05874 PDF


We consider first order variational MFG in the whole space, with aggregative interactions and density constraints, having stationary equilibria consisting of two disjoint compact sets of distributions with finite quadratic moments. Under general assumptions on the interaction potential, we provide a method for the construction of periodic in time solutions to the MFG, which oscillate between the two sets of static equilibria, for arbitrarily large periods. Moreover, as the period increases to infinity, we show that these periodic solutions converge, in a suitable sense, to heteroclinic connections. As a model example, we consider a MFG system where the interactions are of (aggregative) Riesz-type.